The invention relates to the confinement of field-reversed plasma rings produced by a coaxial plasma gun by means of magnetic fields. More particularly this invention relates to the confinement of an accelerated plasma ring by a magnetic mirror.
The magnetic mirror is one approach currently being developed as a future fusion power reactor system. In a mirror system the magnetic field lines enter and leave the confinement chamber at its ends. To prevent end losses the intensity of the field is increased at each end (the mirrors). At the same time the field shape is chosen so as to suppress any tendency of the plasma to escape sideways across the field. The basic concept involved is to produce a magnetic well or a region in space where the plasma particles, trapped in the field lines of the external field, encounter an increasing magnetic field in whatever direction they move. This adiabatic confinement by the magnetic mirror depends on the fact that a particle trapped on and circling about a field line can be thought of as a circular current loop guided by, and in motion along, the field lines. Such a current loop will tend to be repelled from the regions of increasing field, or from the mirror regions. This results in a gyrating motion by the charged particles which are reflected back and forth between the mirror ends.
The simple mirror described above has an inherently low Q (where Q is defined as the ratio of fusion output power to input reaction sustaining power) because ion-ion collisional scattering redirects the ions out through the mirrors. An additional scattering mechanism producing plasma instabilities is the drift cyclotron loss cone (DCLC) mode, the effects of which can be reduced by such techniques as warm plasma stream injection. However, this also reduces the Q-value of the reaction thereby further limiting the commercial feasibility of this approach.
In contrast to the simple mirror approach is the field-reversed mirror (FRM) approach. In the FRM reaction some of the inner magnetic field lines close back on themselves thus creating a region in which plasma ions and electrons are more efficiently trapped. The comparatively rapid angular scattering processes described in the preceding paragraph are not as important in the FRM where the dominant loss process is cross-field diffusion, a much slower process. Substantial increases in attainable Q-value have been predicted for this configuration, e.g., Q-values of up to 5 or more. See Lawrence Livermore Laboratory (LLL) reports UCRL-52170 (1976) and UCRL-52407 (1978) available from the Technical Information Department, Lawrence Livermore Laboratory, Livermore, Calif. 94550.
Recent magnetic mirror experiments have led to unprecedented high values of .beta. (the ratio of plasma pressure to maximum magnetic field pressure) where ##EQU1## with n=plasma density
E.sub.i =mean ion energy PA1 B.sub.vac =vacuum magnetic field strength Values of .beta. greater than unity are reported by B. G. Logan, et al., Phys. Rev. Lett., 37, 1468 (1976). With these increasing .beta. values, improvements in the field reversal factor, .DELTA.B/B, which is defined as the change in field strength at the plasma center .DELTA.B divided by the vacuum field strength B, have also been observed. Field reversal factors as large as 0.9, with values greater than 1.0 representing field reversal at the center of the magnetic mirror cell and values of 2.0 representing total field reversal with the plasma's magnetic field equal in magnitude, but opposite in direction to the applied magnetic field, are reported in Lawrence Livermore Laboratory UCRL-80857 (1978). However, with .DELTA.B/B&lt;1 it can be concluded that in these experiments no closed field lines were produced. These experimental results are compared with theory in LLL preprint report UCRL-80635.
The prior art contains various approaches to achieve field reversal. The more prominent and pertinent approaches include the Astron scheme, field reversed ion rings formed by cusp injection, field reversed theta pinch, and the adiabatic compression of plasma gun injected vortices. Each of these individual approaches is considered in the following paragraphs.
The relativistic electron beam (Astron) approach, as first described by N. C. Christofilos, Proc. of Second United Nations Intl. Conf. on Peaceful Uses of Atomic Energy (United Nations, Geneva, Switzerland, 1958), Vol. 32, 279, involves producing and sustaining field reversal by bulk plasma diamagnetic currents generated by a layer of multi-MeV electrons. This approach is the subject of U.S. Pat. No. 3,664,921. It is to be noted here that in this set of experiments the interior magnetic field was produced by an auxiliary group of particles, namely the relativistic circulating electrons, rather than particles in the main plasma. This confining current was produced by a relativistic electron beam. The magnetic field confinement of this relativistic electron beam proved extremely difficult, which resulted in these experiments being of limited success. Later, Fleischmann et al. utilized this approach by injecting 500 kiloelectron volt, 10 kiloampere electron beams into a magnetic mirror of the Astron geometry to achieve field reversal by producing closed field lines with field reversal factors of up to 1.2 in the mirror's center and lifetimes of up to 20 microseconds. See Fleischmann et al., Phys. Rev. Lett., 29, 256 (1972). Christofilos and Fleischmann both concluded that, although field reversal had been achieved with relativistic electrons, a net power reactor application was unlikely due to excessive synchrotron radiation losses by the electron ring. In addition, these relativistic electron beams have not yet been shown to be able to coexist with a low density, high temperature plasma.
Another approach is described by H. H. Fleischmann and T. Kammash, Nuclear Fusion, 15, 1143 (1975), involving the trapping in an externally applied magnetic field of a field-reversing ring of several hundred MeV protons or deuterons. This scheme envisions the production of the field-reversing rings via the adiabatic compression of low energy (10-20 MeV) ion rings which could be generated by conventional accelerators. However, significant questions regarding the feasibility of this approach were left unanswered by the authors, leaving this approach still to be experimentally verified. These unresolved issues included the gross stability of the projected ion rings thus produced, the interaction of the plasma currents generated along the magnetic field lines with the fast-ion ring and the overall energy efficiency of the ring-producing ion diodes.
The reversed field theta pinch is produced by shock ionization and heating of a gas by a rapidly rising solenoidal magnetic field. If this magnetic field is then rapidly reversed in direction, the trapped flux inside the plasma is now oppositely directed to the applied field, thus producing the field-reversed configuration following reconnection of the magnetic flux lines at the ends of the solenoidal-shaped plasma. While this approach utilizes the diamagnetic currents in the plasma itself to produce field-reversal, it is subject to the rapid growth of rotational instabilities which limit its duration to approximately 30 microseconds. The source of this rotational instability is currently the subject of extensive investigative research, as it has resulted in various questions regarding the commercial feasibility of a net power reactor based upon this pulsed power approach. However, the theta pinch technique, when implemented with a conical plasma gun, has shown that the drifting collection of ions approach to achieve field reversal is feasible. From these results, it is concluded that the drifting ion technique will also be successful in achieving field reversal in a magnetic mirror.
In addition to the aforementioned efforts to achieve field reversal, extensive work in the study of the stability of plasma rings projected into and captured by a magnetic field has been performed. H. Alfven, Proc. of the Second United Nations Intl. Conf. on the Peaceful Uses of Atomic Energy (United Nations, Geneva, Switzerland, 1958), Vol. b 31, 3, and L. Lindberg and C. Jacobsen, Astrophysical Journal, 133, 1043 (1961), describe experiments and the underlying theory in this area. Here a radial magnetic field is produced between a magnetic pole inside a coaxial plasma gun's inner electrode an an annular pole of opposite polarity outside the gun's outer electrode. It was found that the moving plasma ring carries the magnetic field's lines of force with it provided it has a sufficiently high conductivity and density. Upon proceeding further, the plasma ring stretches the lines of force and finally breaks them so that a free plasma ring is produced which moves on. No attempt was made here to confine the ring either in a magnetic mirror or other magnetic well. One would expect the ring-shaped plasma passing the static magnetic field at the gun's muzzle to conserve the magnetic flux through the central electrode of the gun as a poloidal flux through the center of the plasma ring. However, it was observed that the moving ring's poloidal flux was several times larger than the static flux. It was concluded that the increased magnetic flux was due to an instability of the pinched current path in the plasma such that the azimuthal flux in the plasma, initially set up by the discharge current, was transformed into a poloidal flux. These experiments, however, did not utilize a magnetic guide field in the plasma gun tube, nor was a magnetic mirror present for plasma confinement. In addition, the coaxial plasma gun was employed in a relatively low efficiency mode, resulting in the production of very low temperature plasmas with low electrical efficiency.
In summary, successful reversal of the plasma-confining magnetic field has been achieved with relativistic electron beams and by the theta pinch approach. But the relativistic electron beam approach suffers from excessive synchrotron radiation losses while the straight theta pinch technique is plagued by plasma break-up due to rotational instability. While the conical theta pinch technique has successfully produced moving field-reversed rings, this approach suffers from low energy efficiency. The present invention, however, makes use of an extremely efficient energy coupling scheme between the high energy plasma generator and the externally imposed magnetic field which results in the conservation of the plasma's confining magnetic flux and facilitates achieving field reversal in a magnetic mirror confined plasma.